Absolute Magnitude Calculate the absolute magnitude of an object from its apparent magnitude.
By Colin Gaudion – see his original here

Zenith Angle Work out the Zenith Angle. More info on Wikipedia: https://en.wikipedia.org/wiki/Zenith
By Colin Gaudion – see his original here

Focal Ratio Use the aperture and focal length to work out the focal ratio.
By Colin Gaudion – see his original here

Airmass From Zenith Angle to Airmass
By Colin Gaudion – see his original here

Plate Scale For helping you convert between the size of the image magnified through a telescope and its actual size.
By Colin Gaudion – see his original here

Stellar Parallax Stellar Parallax – for working out the distance of a star based on the difference when you compare its angle in the sky between opposite sides of our orbit around the sun.
By Colin Gaudion – see his original here

Julian Day Convert from Gregorian Calendar (the one most of us use) to Julian Day.
By Colin Gaudion – see his original here

The Drake Equation The Drake Equation – for estimating the number of planets with intelligent life in the milky way.
By Colin Gaudion – see his original here

Maths & Science

Efficiency of your phone or laptop charger Have you ever wondered how efficient your phone or laptop charger is?
If you look at the tiny writing on the charger it gives you a few numbers that help you work it out.
They look a bit like this:
To work out the efficiency, you’re looking for the input voltage, input current, and output voltage and output current, highlighed in yellow above.
The input voltage might be in mA (milli-Amps), so to convert that to Amps, simply divide by 1,000.
In this case, both input and output currents are in Amps, so can enter the numbers as they appear.
For this one, the input voltage is a range (100-240V), so you can enter that range directly in the Livesheet (as has been done by default in the form below).
Try entering the numbers for some of yours and see how they look.
I’ve found that 25% seems to be fairly typical.

A number rounded to x significant figures If you want to round a number to a certain number of significant figures, there is no built-in function for this.
This Livesheet will do it for you. Just enter the number and how many significant figures you want to round to. The default number of significant figures is 1.

e^x Taylor Series Expansion This livesheet tells you the Taylor series expansion for ex , to the number of terms you specify, and tells you what the next term is.

Force between two charged particles To calculate the force between two charged particles, using Coulomb’s Law, add the strengths of the two charges and the distance between them.
The resulting force is the repulsive force; that is, the force pushing them away. A negative number is an attractive force pulling them together.
You can enter numbers in scientific format as well as in standard format. For example, for 1.5 x 1015 enter 1.5e15.

Numbers in Exponent Form For working with numbers in the ‘scientific’ exponent form.
This converts an exponent form into a number:
And this converts a number into an exponent form:
Exponent form is actually text, so if you are using it in a calculation you need to convert it into a number before doing anything with it. You can convert it back to exponent form when you want to display it.
Numbers are currently accurate only to the 16th significant figure, so you may find strange numbers appear after that point. We hope to fix this problem soon.

Fix Decimal Places Fix the number of decimal places (in other words, add trailing zeros if a number doesn’t have the number of decimal places you need).

Geometric Mean Find the Geometric Mean of two numbers.
This is useful for estimating. If you have an idea of the low and high range of a value you are trying to estimate, this gives you the central value which is the same factor away from both the low and high estimate.
Or you can calculate the geometric mean of any number of numbers in the form below, by entering them in the box separated by commas.

Sum of a geometric series Use this to add up any number of terms in a geometric series (a geometric series is one where to calculate each term you multiply the previous term by the same number).
Or – find the sum over an infinite number of terms:

Arctan An annoying oversight in Livesheets is the lack of inverse trig functions. They will be turning up in the new version, when it’s complete. But in the mean time, this sheet calculates the arctan of a number (in radians) using a polynomial expansion.
This gives you the option to choose how many terms you want to go to in your expansion (the more you use, the slower it will be). 11 or so seems to be enough for most values. For numbers close to 1 or -1, it seems to need more, perhaps going to 50 or so.

Calculating Electrical Power from Voltage, Resistance, Current In order to calculate electrical power consumption, you need any two of three pieces of information:
Voltage (measured volts)
Current (measured in amps)
Resistence (measured in ohms).
This calculator lets you enter the ones you know and calculates the power using all three methods.

Interpret Complex Numbers Type your complex number (for example 1+i, or 2.5-6i), and this will tell you the size of the real and imaginary parts.

Median Average This node works best as a component – click ‘Use This’ to import it into your space if you have an account.
Enter a list of numbers and it will tell you the median average.

Modulus Find the modulus of a number with a chosen modulo.
(This tells you what the remainder would be if you divided it by the modulo). It is needed because the built in mod function doesn’t always work.

Haversine Find the haversine of an angle (in radians)
(used for trigonometry on spheres)

Circular Arc Length Input the radius (in any unit) of a circular arc and the angle subtended at the centre (in degrees) to calculate the arc length. The answer will have the same units as the radius.
Created by Navino Evans

Area of a Circle Input the radius of a circle to calculate its area. You can use any unit you like for the radius to get the area in square units. For example, enter the radius in metres and the area will be in square metres.
Created by Navino Evans

Area of a Triangle Input the base and height of a triangle to calculate its area. Make sure that the base and height are at right angles to each other. You can use any units you like (but must be the same unit for both measurements). The area calculated will be in square units.
Created by Navino Evans

Surface Area of a Sphere Input the radius of a sphere to calculate its surface area. You can use any unit you like for the radius to get the surface are in square units. For example, enter the radius in metres and the volume will be in square metres.
Created by Navino Evans

Volume of a sphere Input the radius of a sphere to calculate its volume. You can use any unit you like for the radius to get the volume in cubic units. For example, enter the radius in metres and the volume will be in cubic metres.
Created by Navino Evans

Newton’s Law of Universal Gravitation – Calculate the force between two masses Calculate the gravitational force (in Newtons) between two point masses (in Kilograms) separated by a distance (in Metres). The force on each mass will have the same magnitude and act along the line joining them. This function can also be used to calculate the approximate force between two bodies with spatial dimensions by using the distance between their centres of mass.
Created by Navino Evans

How much energy does it use when you leave the hot tap running? Enter the amount of time it is running for, and the starting and ending temperatures of the water, and it will tell you approximately how much energy it is using up to keep the hot tap running.
7°C is a good bet for starting temperature in winter in the UK, perhaps more like 15°C to 20°C in the summer; and usually the hot tap will produce water at about 60°C.
And, in terms of money. The current prices can be found on this USwitch Calculator. At the time of writing, electricity is 13.55p/KwH and gas is 4.162p/KwH on standard tariffs.
SourcesHow much water used per minute when you leave the tap running?Volumetric Heat Capacity of Water at 25°C(This calculation approximates by using the heat capacity of water at 25°C rather than taking account of the change in heat capacity with temperature, but it is accurate to within less than 1%).

Binomial Theorem Combinations Calculator nCr and nPr Calculators.
This is used to work out how many possible combinations or permutations there are if you want to choose r items out of a set of n.
First, the number of combinations (in other words, the order in which you choose them doesn’t matter).
Second, the number of permutations (the order in which you pick them does matter)

Black body radiation – Temperature to max Wavelength For a theoretical ‘black body’, this uses the Temperature (in Kelvin) to tell you the wavelength of peak intensity at that temperature (in metres).
Or, use the wavelength of peak intensity (in metres) to find the temperature (in kelvin)
To convert between kelvin and celsius, see here: http://livesheets.com/gallery/unit-conversion-gallery/kelvin-celsius-conversion/
To convert between wavelength and frequency, see here: http://livesheets.com/gallery/mathematics/convert-wavelength-to-frequency-for-light-in-travelling-in-space/

Solve Simultaneous Equations Use Livesheets to solve simultaneous equations. Just type two equations in terms of x and y, and get the answer. Simple as that.

Divide two numbers with units Divide one number by another – with units.
Use it by entering the number, then an inverted comma (‘), then whatever units you want. Multiply units by separating them with a dot (.) and divide them by separating them with a slash (/).
For example, for 6 metres per second, you would write:
6′m/s
For 2 watts per square metre per second, you would write:
2′w/m.m/s

Multiply two numbers with units This allows you to multiply two numbers with units, and it will tell you the resulting number and tell you the units.
Use it by entering the number first, then the inverted comma symbol (‘), then whatever units you want. Multiply units by separating them with a dot (.) and divide them by separating them with a slash (/).
For example, for 6 metres per second, you would write:
6’m/s
For 2 watts per square metre per second, you would write:
2’w/m.m/s

Find the average speed Enter the distance covered and the time taken, and find the average speed.
For the distance you can use any units, and the result will be in the same units. For example, if you enter the number of kilometres, the result will be in kilometres per hour. If you use miles, it will be in miles per hour.

Angled Trajectory of a Projectile Enter the launch velocity, angle of launch, launch height and landing height, and find out the projectile’s maximum height, when it will land, and how far it will have travelled (assuming no air resistance)

Vertical Trajectory Enter the initial velocity and start and end heights, and find out the landing time and the maximum height reached (assuming no air resistance):

Compound Interest Calculator Enter the initial value, rate of growth or interest, and number of time periods, and it will tell you the final value.

Mach Number In Air Enter Speed (metres per second) and Temperature (°C), and find the Mach Number in Air:

Converting time between time zones Enter the time in the first zone, along with the time zone, and find out what the equivalent time is in a different time zone.
You can enter the time Like: 4:30pm or 430pm or 1630 or 16.30.

MPH to km/h and Mach Number In honour of Felix Baumgartner’s record-breaking jump from space, here is a Livesheet to convert from his top speed of 833.9 MPH to the equivalent in km/h and also the Mach Number (how many times the speed of sound).

Ounces/Grams Conversion Enter the number of ounces, find out the equivalent number of grams:
Enter the number of grams, find the equivalent number of ounces:

Cups/Grams Conversions Enter the number of US Cups, find out the equivalent number of grams for
Plain Flour (or all purpose flour):
Butter:
Granulated Sugar:
Packed Brown Sugar:
Chocolate Chips:
Chopped Nuts:

Cups / ml Conversion Enter the number of Cups, find the equivalent number of millilitres:
Enter the number of millilitres, find the equivalent number of Cups:

Kelvin / Celsius Conversion Enter the temperature in Kelvin, find out the equivalent in Celsius:
Enter the temperature in Celsius, find out the equivalent in Kelvin:

Celsius / Farenheit Conversion Enter the temperature in Celsius, find out the temperature in Farenheit:
Enter the temperature in Farenheit, find out the temperature in Celsius:

Astronomical Units to Kilometres Conversion Enter the number of Astronomical Units (AU) and find out the equivalent number of kilometres. Useful if you’re thinking of going on an interplanetary journey by car (Mars is only about 0.7AU if you go at the right time of year).

Inverse VAT This allows you to enter the total amount and find out how much VAT was and what the amount was before VAT. Based in the current UK VAT rate of 20%.

Invoicing – Calculate Subtotal, VAT and Total This is for preparing invoices.
Enter the amounts of all the individual items on your invoice (separated by spaces as shown in the example) and this form will tell you the subtotal, the VAT, and the Grand Total.

Inflation Calculator Find out how much an amount of money in one year would be worth in another. Based on the Retail Prices Index (RPI) and valid for years between 1947 and 2013.

What classes of national insurance do you pay? Answer the questions and it will tell you which classes of national insurance you are liable for (valid for people working in the UK).
This excludes Class 3 contributions, which are voluntary contributions for people who would not otherwise pay any national insurance.

Uk Income Tax 2013-14 Enter your age and income and you can see how much is in each band and how much tax is due to be paid in total.

US Consumer Price Index Enter the year (from 1913 to 2012) and find the average value of the consumer prices index for the US Dollar for that year.

Historical USD / GBP exchange rates Enter the year and find out the annual average spot exchange rate for that year (any year from 1975 to 2012). It tells you how many US Dollars you could have bought with £1.

Inflation since 1947 Find the inflation index values in previous years.
Retail Price Index (RPI) since 1947. The retail price index calculation was re-based at at value of 100 several times during this period, so the published figures are difficult to track. This calculation adjusts for that and shows how much money you would need to have the equivalent spending power of £100 in 1947.
In 1998 and additional measure, the Consumer Price Index (CPI) was introduced. This provides the CPI based at 100 in 2005, so it tells you how much money you would need in the given year to have the equivalent spending power of £100 in 2005.

Cost of electricity At today’s price 28th March 2013, on the EDF standard tariff, the price of electricity is 13.55p per KwH.
Enter the number of KwH and the price of electricity if different, and it will tell you the total cost.

How much energy does it use when you leave the hot tap running? Enter the amount of time it is running for, and the starting and ending temperatures of the water, and it will tell you approximately how much energy it is using up to keep the hot tap running.
7°C is a good bet for starting temperature in winter in the UK, perhaps more like 15°C to 20°C in the summer; and usually the hot tap will produce water at about 60°C.
And, in terms of money. The current prices can be found on this USwitch Calculator. At the time of writing, electricity is 13.55p/KwH and gas is 4.162p/KwH on standard tariffs.
SourcesHow much water used per minute when you leave the tap running?Volumetric Heat Capacity of Water at 25°C(This calculation approximates by using the heat capacity of water at 25°C rather than taking account of the change in heat capacity with temperature, but it is accurate to within less than 1%).

UK Universal Income Tax Calculator The UK has some slightly unusual income tax rules, so this is a universal calculator which lets you input the rules for any year and find the tax.

What will your savings be worth? Want to know what your savings will be worth in the future?
Enter the current amount, the amount of interest, and the number of years, and it will tell you what they’ll be worth.

2013-14 vs 2012-13 UK Income Tax Comparison Enter your income and see what the difference will be in your tax between 2012-13 and 2013-14.
This was built to demonstrate Labour party leader Ed Miliband’s claim that millionaires would be given a £40k tax break by the current Government. Technically, he meant people earning £1m a year, so it’s seeded with a default of £1m.

UK 2012-13 Budget Balancer We were offered a chance to present Livesheets to the British Chancellor of the Exchequer George Osborne and created this for the occasion – a 2012-13 UK Budget Balance to help him balance the books.
It defaults to the current values and allows you to see the effect of changing the sizes of the various Government Departments.

Food & Health

Adjusting the baking time If you’re baking using a different sized baking tray from the one recommended by the recipe, this will tell you what your adjusted baking time should be.

Adjusting the quantities in a recipe Enter the total amount the recipe makes and the total amount you want to make, and then you can enter the amount in the recipe for each ingredient and see how much you should use.

A number rounded to x significant figures If you want to round a number to a certain number of significant figures, there is no built-in function for this.
This Livesheet will do it for you. Just enter the number and how many significant figures you want to round to. The default number of significant figures is 1.

Convert text into CamelCase Convert text into CamelCase. CamelCase is where separate words are strung together without spaces and with the first letter of each word capitalised.
The first letter can be capitalised or not, it’s your choice.

Default Number To use when you want a default number, in case the user doesn’t enter one. If you click ‘Use This’ to import it as a component, you can also use it for text or any other data types.

Group Digits Group digits with a “,” or “.” (English style or European style).
Simply enter the number and the character you want to group it with.
The output is text, so watch out for that. You you’ll have to convert it to a number before you can use it.

Inflation Calculator Find out how much an amount of money in one year would be worth in another. Based on the Retail Prices Index (RPI) and valid for years between 1947 and 2013.

Numbers in Exponent Form For working with numbers in the ‘scientific’ exponent form.
This converts an exponent form into a number:
And this converts a number into an exponent form:
Exponent form is actually text, so if you are using it in a calculation you need to convert it into a number before doing anything with it. You can convert it back to exponent form when you want to display it.
Numbers are currently accurate only to the 16th significant figure, so you may find strange numbers appear after that point. We hope to fix this problem soon.

Fix Decimal Places Fix the number of decimal places (in other words, add trailing zeros if a number doesn’t have the number of decimal places you need).

Convert Gmail “Show Original” URL to normal view When viewing a message in Gmail, there is a drop-down menu next to each message which contains an option labelled “Show Original”.
This gives you a permalink to a message but shows the full headers. Go obtain a Gmail message permalink, click “Show Original”, then paste the URL into this form to see get a permalink URL which will show the message in a normal view.

Get URL From Google Link If you try to copy a link from Google search results, it gives you a long and complicated URL that starts something like:
https://www.google.co.uk/url?sa=…
It’s clearly not the URL you are looking for when you went to ‘Copy Link Address’.
This calculator lets you enter that long Google link and strips it down to find the actual link you were looking for.

Arctan An annoying oversight in Livesheets is the lack of inverse trig functions. They will be turning up in the new version, when it’s complete. But in the mean time, this sheet calculates the arctan of a number (in radians) using a polynomial expansion.
This gives you the option to choose how many terms you want to go to in your expansion (the more you use, the slower it will be). 11 or so seems to be enough for most values. For numbers close to 1 or -1, it seems to need more, perhaps going to 50 or so.

Make sure a list is the right length (if not truncate it or extend it) This component needs to be imported to make sense (make sure you have an account and click ‘Use This’ in the bottom right to import it).
Add a list and tell it how long you need the list to be and it will either truncate it to the required length, or extend it to the required length by copying the last item.

Interpret Complex Numbers Type your complex number (for example 1+i, or 2.5-6i), and this will tell you the size of the real and imaginary parts.

Median Average This node works best as a component – click ‘Use This’ to import it into your space if you have an account.
Enter a list of numbers and it will tell you the median average.

Match and Return for text or exact matches This is like vlookup in Excel. It lets you enter a list of numbers of strings of text, and a single item, and will return the item in a second list which corresponds with the matching item in the first list.
Unlike the other vlookup-equivalent node (which only works for numbers and matches the first value that is higher than the one entered), this will only give you a result if there is an exact match, and in this case works for text as well as numbers.
Click ‘Use This’ to import it into your space, if you have an account.

Enter any units you want and convert them into a primary unit This is a useful component when you want to allow other people to enter their own units.
It’s best used by pressing ‘Use This’ to import it into your space.
You can then add the number and units in the first box, the list of units in the second box, and the corresponding list of multiples in the third box, and it will then give you your number in the primary unit (the one which has the multiple of 1).
You can enter up to 2 units at any time. For example you could add units of both lb and oz, and then type “2lb 3oz” into the box. Spaces are always ignored.

US Consumer Price Index Enter the year (from 1913 to 2012) and find the average value of the consumer prices index for the US Dollar for that year.

Cost of electricity At today’s price 28th March 2013, on the EDF standard tariff, the price of electricity is 13.55p per KwH.
Enter the number of KwH and the price of electricity if different, and it will tell you the total cost.

Black body radiation – Temperature to max Wavelength For a theoretical ‘black body’, this uses the Temperature (in Kelvin) to tell you the wavelength of peak intensity at that temperature (in metres).
Or, use the wavelength of peak intensity (in metres) to find the temperature (in kelvin)
To convert between kelvin and celsius, see here: http://livesheets.com/gallery/unit-conversion-gallery/kelvin-celsius-conversion/
To convert between wavelength and frequency, see here: http://livesheets.com/gallery/mathematics/convert-wavelength-to-frequency-for-light-in-travelling-in-space/

Adapting the quantities of ingredients This works best when imported into Livesheets by using the ‘Use This’ button.
Add a list of ingredients as an input, then the base amount and the amount you want, and it will adjust all of the quantities.
To use it, you need the number at the beginning, then a space (for example, if write “100 g flour”, not “100g flour”. If there is no quantity, that’s fine (eg. “a pinch of salt”).
For quantities less than 2, it tries to give you the amount as a fraction (eg. 1/2 onion).

More than or equal to For a single comparison you can use ‘>=’ for more than or equal to, but if you want to apply it to a list, that doesn’t work. Instead, you can use this.

Significance Round to the nearest number of significance.
For example, if you round 1.1111 to a significance of 0.1, it will give you 1.1.

Internal Rate of Return An approximation of Internal Rate of Return, for when you have one outgoing amount followed by a series of incoming amounts.
This is designed for use inside Livesheets so it doesn’t really work as a form. Instead, use it by signing up for an account, then clicking on Use This, to import it into your space.
Just enter the outgoing amount in the first box and the incoming amounts as a list in the second box.

Net Present Value This is a Livesheet which relies on a list as an input so can only inside another livesheet, but you can use it by clicking on the Use This button to import it into your space.
Just input the discount rate per period and the list of payments, and it will give you the net present value.

Difference between dates For finding the number of days between two dates.
It is accurate for dates from 1st January 1AD.
Just enter the two dates in dd/mm/yyyy format

Interpret Dates To pick apart a date from dd/mm/yyyy format into three separate numbers

Livesheets VLookup Equivalent This Livesheet is the full equivalent of VLookup.
Unfortunately it doesn’t work as a web form, but you can Use it by clicking on Use This, and then make use of it within your own livesheets.
To use it, enter the lookup value in the first box, the list of values you want to match it against in the second box (in ascending order), and the corresponding list of values you want to pick a result from in the third box.
It looks for the first answer that is higher than the lookup value and returns the corresponding return value. If the lookup value is higher than or equal to all the values in the second box, it returns the (n+1)th item in the return list if it exists. This means the return list can be one longer than the lookup list.

Value is less than which row? If you click the button to Use This, you can use it a bit like a vlookup in Excel.
Unfortunately, you can’t use this in the form version though, you have to Use it.
Enter a value in the first box and an ascending list of values in the second. It will tell you the number of the first row which is larger than the entered value.
For example, if you enter 10, and the values 9, 11, 13, it will return the number 2 (because 10 is less than the 2nd value in the list).

Combine and sort two comma separated lists Enter two comma separated lists, see them combined and sorted.
Items in the list are also trimmed (spaces removed from the beginning and end), and items of zero length are removed.

Get URL From Google Link If you try to copy a link from Google search results, it gives you a long and complicated URL that starts something like:
https://www.google.co.uk/url?sa=…
It’s clearly not the URL you are looking for when you went to ‘Copy Link Address’.
This calculator lets you enter that long Google link and strips it down to find the actual link you were looking for.

Traffic Engineering – Saturation Flow This is for doing a quick calculation of saturation flow (how fast traffic flows through a junction) for traffic engineers.
Enter a comma separated list of the number of PCUs of saturated flow in each green time in the first list; and a comma separated list of the corresponding lengths of the saturated periods (in seconds) in the second list, and it gives you the answer.

Crowd Flow Calculation This is for working out how long it will take for people to exit from an area of a stadium.
You enter the number of people using the vomitory and it tells you how long it will take for everyone to get out.
Need that in hours, minutes and seconds? Here you go: